Universal properties at the onset of chaos in diode resonator systems

Complexity and transition to chaos in coupled Adler-type oscillators

Coupled nonlinear oscillators are ubiquitous in dynamical studies. A wealth of behaviors have been found mostly for globally coupled systems. From a complexity perspective, less studied have been systems with local coupling, which is the subject of this contribution. The phase approximation is used, as weak coupling is assumed. In particular, the so-called needle region, in parameter space, for Adler-type oscillators with nearest neighbors coupling is carefully characterized. The reason for this emphasis is that, in the border of this region to the surrounding chaotic one, computation enhancement at the edge of chaos has been reported. The present study shows that different behaviors within the needle region can be found and a smooth change of dynamics could be identified. Entropic measures further emphasize the region's heterogeneous nature with interesting features, as seen in the spatiotemporal diagrams. The occurrence of wave-like patterns in the spatiotemporal diagrams points to nontrivial correlations in both dimensions. The wave patterns change as the control parameters change without exiting the needle region. Spatial correlation is only achieved locally at the onset of chaos, with different clusters of oscillators behaving coherently while disordered boundaries appear between them.

Computational capabilities at the edge of chaos for one dimensional systems undergoing continuous transitions

While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular automata, there is an enhancement of computation capabilities as the system moves towards cellular automata with chaotic spatiotemporal behavior. The computation capabilities are followed by looking into the Shannon entropy rate and the excess entropy, which allow identifying the balance between unpredictability and complexity. Enhanced computation power shows an increase of excess entropy, while the system entropy density has a sudden jump to values near one. The analysis is extended to a system of non-linear locally coupled oscillators that have been reported to exhibit spatiotemporal diagrams similar to cellular automata.

Intermittency-induced criticality in a resistor-inductor-diode circuit

The current fluctuations of a driven resistor-inductor-diode circuit are investigated here looking for signatures of critical behavior monitored by the driving frequency. The experimentally obtained time series of the voltage drop across the resistor (as directly proportional to the current flowing through the circuit) were analyzed by means of the method of critical fluctuations in analogy to thermal critical systems. Intermittent criticality was revealed for a critical frequency band signifying the transition between the normal rectifier phase in the low frequencies and a full-wave conducting, capacitorlike phase in the high frequencies. The transition possesses critical characteristics with a characteristic exponent p_{l}=1.65. A fractal analysis in terms of the rescale range (R/RSS) and detrended fluctuation analysis methods yielded results fully compatible with the critical dynamics analysis. Suggestions for the interpretation of the observed behavior in terms of p-n junction operation are discussed.